7. Cost of Dog Ownership. Money reports that the average annual cost of the first year of owning and caring for a large dog in 2017 is $1448. The Irish Red and White Setter Association of America has requested a study to estimate the annual first-year cost for owners of this breed. A sample of 50 will be used. Based on past studies, the population standard deviation is assumed known with s = $255.

a. What is the margin of error for a 95% confidence interval of the mean cost of the first year of owning and caring for this breed?

b. find the margin of error at 99% confidence.

49. Family Vacation Expenses. A survey conducted by the American Automobile Association showed that a family of four spends an average of $215.60 per day while on vacation. Suppose a sample of 64 families of four vacationing at Niagara Falls resulted in a sample mean of $252.45 per day and a sample standard deviation of $74.50.

a. Develop a 95% confidence interval estimate of the mean amount spent per day by a family of four visiting Niagara Falls.

b. Based on the confidence interval from part (a), does it appear that the population mean amount spent per day by families visiting Niagara Falls differs from the mean reported by the American Automobile Association? Explain.

c. Find the confidence interval at 99% confidence.Does your answer to part b change as a result of being more confident?

53. Obesity. Obesity is a risk factor for many health problems such as type 2 diabetes, high blood pressure, joint problems, and gallstones. Using data collected in 2018 through the National Health and Nutrition Examination Survey, the National Institute of Diabetes and Digestive and Kidney Diseases estimates that 37.7% of all adults in the United States have a body mass index (BMI) in excess of 30 and so are categorized as obese. The data in the file Obesity are consistent with these findings.

a. Assume you sample 40 people, what is the margin of error for those with a BMI of more than 30 at 90% confidence?

b. Holding all else constant, you are able to increase the sample size to 100 individuals, what is the new margin of error?

c. Discuss the change and cause of the change in your answers to a and b.